Well, I usually take this kind of writing as granted because I live in Japan. But I found the style interesting for the first time in my life. I know it is challenging to make this kind of letter for not only non-native people but also inexperienced native people. What I don't know is that if it's difficult to read? It might sound an odd question though.

I think that this would not be difficult for anyone properly prepared for honorific/humble forms commonly used in commercial interaction and cordial forms common in written correspondence. The topics are directly addressed, as expected in written correspondence, and since negotiations have been completed and discussion of financial details intended for another time.

I was a little surprised by how difficult I found it to read. I don't normally read this kind of writing at all (except for the rare email from a Japanese online store or something I don't have much contact with "professional" language), so I guess it's to be expected...

益々 - I can't remember seeing ますます written this way before.
ご清祥 - I was totally unfamiliar with this.
発注 - I only knew 注文 ...
内示 - ah, "unofficial/private" notification. I assumed "internal" notification for some reason.
掲記 - this has no entry in EDICT, Kenkyusha, or either of the JE dictionaries on Yahoo!. 大辞林・大辞泉 have it though.
存じます - I was only familiar with 存じる meaning 知っています, and not meaning（と）思います.
つきましては - I've heard it before, but I never really knew what it meant.
賜る - this is on my study list but words like 賜る、奉る、承る、I keep forgetting because I never see them!

Thank you Hektor6766-san and Hyperworm-san for your helpful information. I understand both of you.
Interestingly, your opinions are almost the same as mine. This kind of writing is very difficult in a way because of those unfamiliar terms, but it usually doesn't bother us a lot because the meaning/intention itself is very simple as Hektor6766-san said.
For instance, if one of you asked the meaning/definition of ご清祥 to ten Japanese people, nine out of ten would need to look it up in a dictionary. (I personally think coco-san would be one of the ones who don't need the dictionary.) I haven't heard of the word 掲記 like Hyperworm-san. However, when we read it, we don't care. We read the context. And in order to do that, we pick up only the few key kanji (not words).

さて、この度は掲記の件に関しまして、弊社に発注のご内示を下さいましてありがたく厚くお礼申し上げます。
Well /,/ this time / subject above / regarding /,/ to our company / order / notice / gave / thanks / very / appreciate / tell you

That is a knack to read this kind of writing. In most cases, the readers are not expected to "understand" every single word even if it's a question sentence in the JLPT-1 test.

Well, I'm not sure if it would be useful information though. Because it was my first time to see a typical Japanese business letter from a perspective viewpoint, I found it interesting and posted that.